Ideals in L(L1)
Abstract
The main result is that there are infinitely many; in fact, a continuum; of closed ideals in the Banach algebra L(L1) of bounded linear operators on L1(0,1). This answers a question from A. Pietsch's 1978 book "Operator Ideals". The proof also shows that L(C[0,1]) contains a continuum of closed ideals. Finally, a duality argument yields that L(∞) has a continuum of closed ideals.
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